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Notes on frequencies and timescales in nonequilibrium Greens functions

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 Added by Takaaki Ishii
 Publication date 2016
  fields
and research's language is English
 Authors Takaaki Ishii




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We discuss the ringdown behavior of the nonequilibrium Greens function in a strongly coupled theory with the holographic dual with a focus on quasinormal-mode equilibration. We study the time resolved spectral function for a probe scalar in Vaidya-AdS spacetime in detail as a complement to the preceding work arXiv:1603.06935 using further numerical results in very nonadiabatic temperature changes. It is shown that the relaxation of the nonequilibrium spectral function obtained through the Wigner transform is governed by the lowest quasinormal mode frequency. The timescale of the background temperature change is also observed in the frequency analysis. We then consider a toy model motivated by the quasinormal mode behavior and discuss these main features in numerical results are simply realized.



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The thermal one- and two-graviton Greens function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the t Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.
We investigate a new property of retarded Greens functions using AdS/CFT. The Greens functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar to the pole-skipping phenomenon in holographic chaos. Our examples include the bulk scalar field, the bulk Maxwell vector and scalar modes, and the shear mode of gravitational perturbations. In these examples, the special points are always located at $omega_star = -i(2pi T)$ with appropriate values of complex wave number.
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An approach is outline to constructing an optical potential that includes the effects of antisymmetry and target recoil. it is based on the retarded Greens function, which could make it a better starting point for applications to direct nuclear reactions, particularly when extended to coupled channels. Its form retains a simple connection to folding potentials, even in the presence of three-body forces.
We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling $Z_{2}$ Ising model, sinh-Gordon model and $Z_{3}$ scaling Ising model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.
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